Explore stress-strain curves for different materials. Identify yield point, ultimate strength, and fracture with interactive annotations.
Select a material and this tool draws its engineering stress-strain curve with the points that matter marked - yield strength, ultimate tensile strength, and fracture - plus the elastic line whose slope is Young's modulus. The annotations are interactive: move along the curve to read exact stress and strain at any location, including the straight elastic region and the post-ultimate falling segment. The thing most users get wrong: yield is not always a visible knee in the curve. Aluminum and many alloys yield gradually, so their yield point is fixed by the 0.2% offset construction, a line drawn parallel to the elastic region at 0.2% strain.
A concrete input and expected output from the current implementation.
Input
Steel test bar: gauge length 50 mm, cross-section 100 mm², load 20 kN, measured elastic elongation 0.05 mm.
Expected output
Stress = 20,000 N / 100 mm² = 200 MPa. Strain = 0.05 mm / 50 mm = 0.001 (0.1%). Elastic modulus = 200 MPa / 0.001 = 200,000 MPa = 200 GPa. The point plots on the straight elastic line of the steel curve, and the slope matches steel's textbook modulus.
Stress and strain are both built from original dimensions, so the numbers come straight from the definitions. Their ratio falls at 200 GPa, the expected modulus for structural steel, which confirms the load stayed inside the elastic region rather than past yield.
Stress is force divided by the original cross-sectional area, and strain is elongation divided by the original gauge length, so both values are built on initial dimensions. The elastic portion of the curve is a straight line, and its slope is Young's modulus in the same units as stress. Hovering or moving a marker along the curve returns stress and strain read off this construction, with strain commonly shown as a percentage.
Yield is where permanent deformation begins: the end of the elastic line, or the intersection of a line drawn parallel to the elastic region and offset by 0.2% strain, for materials without a clear yield plateau. Ultimate strength is the highest stress on the curve, where necking starts. Fracture is the final point, where the specimen separates. Between ultimate and fracture the curve falls because engineering stress divides by the original area while the neck keeps shrinking.
The plot uses engineering stress, which divides load by the original cross-sectional area. Once necking starts, the neck shrinks faster than the load grows, so stress computed on the original area falls even though the material itself is still getting stronger. A true-stress curve, computed with instantaneous area, keeps rising to the moment of fracture.
Only approximately. The tool displays values from published material data - typical values or standard minimums - and real behavior depends on your batch's heat treatment and cold work, the specimen geometry, and the strain rate. Use the annotations for design and comparison, and treat a measured mismatch of several percent as normal.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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