Educational reference, not a calculator: Select a material to see its qualitative engineering stress-strain curve with the real, distinct regions labeled — elastic region, yield (or 0.2% offset), strain hardening, and fracture — using approximate values from ASTM/ACI reference properties. Drag the slider to move a marker along the curve and read off stress/strain at that point.
Mild structural steel (ASTM A36, A992) is the textbook ductile material: a long linear-elastic region, a sharp, distinct yield point, an extended yield plateau, then strain hardening to an ultimate stress well above yield before necking and fracture. That reserve ductility — the gap between fy and Fu, and the large strain to rupture — is why steel structures give visible warning (large deflections) before a tension failure, and why AISC 360 LRFD design leans on this predictable, well-defined yield behavior.
Compare how mild steel, concrete, aluminum, and wood actually behave under load — an interactive reference showing the real qualitative shape of each material's engineering stress-strain curve, with the distinct regions (elastic, yield or 0.2% offset, strain hardening, fracture) labeled and explained using approximate ASTM/ACI reference values. This is a learning tool, not a numeric design calculator.
Select a material to load its representative stress-strain curve. Hover or click a labeled region (in the Curve Regions panel or directly on the chart) to see what physically happens to the material in that zone. Drag the slider beneath the chart to move a marker along the curve and read the interpolated stress and strain at that position, along with which region it falls in.
Mild steel (ASTM A36/A992) is the archetypal ductile material: a long linear-elastic region up to a sharp, distinct yield point, then a flat yield plateau, then strain hardening to an ultimate stress well above yield, and finally necking before fracture around 18–21% elongation.
Concrete has no yield plateau at all — its curve is parabolic from the start (stiffness degrades continuously from microcracking), peaks at f’c around a strain of 0.002, and then descends as the material crushes. ACI 318 caps the usable ultimate strain at εcu = 0.003. Because concrete alone offers essentially no ductility, reinforced concrete design depends on the embedded steel reinforcement to provide ductile warning.
Aluminum is ductile like steel but has no sharp yield point — the curve simply rounds over smoothly. Since there is no natural kink to call "yield," ASTM E8 defines yield strength using the 0.2% offset method: draw a line parallel to the elastic modulus, offset by a strain of 0.002 (0.2%), and take its intersection with the measured curve as the offset yield strength.
Wood loaded parallel to the grain is close to linear-elastic almost to failure, with only slight rounding from local fiber crushing near the peak, and then fails abruptly and brittlely — with strength and stiffness that vary substantially by species, grade, moisture content, and defects like knots.
Elastic region — stress is proportional to strain (Hooke’s Law, σ = Eε); deformation here is fully recoverable. Proportional limit / yield (or 0.2% offset for materials without a sharp yield) — the practical boundary between recoverable and permanent deformation. Strain hardening — stress climbs again as the internal microstructure reorganizes (steel and aluminum only; concrete and wood do not show this). Necking / crushing / fracture — the final failure mode, which differs sharply by material: ductile necking with large local strain (steel, aluminum) versus sudden brittle crushing or rupture with little warning (concrete, wood).
Stress (σ) is internal force per unit cross-sectional area (units: ksi, psi, or MPa). Strain (ε) is the dimensionless ratio of deformation to original length (in/in). The stress-strain curve plots how a material’s internal resistance (stress) changes as it’s progressively deformed (strain), and its slope in the elastic region is the modulus of elasticity E.
Concrete is a brittle composite of aggregate and cement paste. Unlike steel’s crystalline lattice, which can plastically deform through dislocation slip, concrete fails by progressive microcracking and eventual crushing of the paste/aggregate matrix — there is no analogous mechanism for a flat plastic plateau. This is precisely why reinforced concrete design (ACI 318) relies on embedded steel reinforcement, not the concrete itself, to provide ductility.
Some ductile materials — notably aluminum alloys — don’t show a sharp break between elastic and plastic behavior; the curve just rounds over gradually. ASTM E8 standardizes an artificial yield definition: draw a line parallel to the elastic modulus, offset by a strain of 0.002 (0.2%), and the stress where that line crosses the measured curve is reported as the "0.2% offset yield strength." It gives engineers a consistent, repeatable yield value to design with even without a natural yield point.
Necking is localized, rapid cross-sectional narrowing that begins once a ductile material reaches its ultimate tensile stress. Engineering stress is calculated as load divided by the ORIGINAL cross-sectional area, so once the neck’s actual area shrinks faster than the load can rise, the plotted (engineering) stress falls — even though the true stress at the neck continues to increase until fracture.
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