Hooke's Law • Yield • UTS • Material Properties — Learn • Explore • Practice • Quiz
Click any region below to highlight it on the diagram. Drag the purple dot along the curve to see live σ and ε values.
The stress-strain diagram is one of the most fundamental tools in mechanical engineering and materials science. It describes how a material responds to applied forces, revealing critical properties such as stiffness, strength, ductility, and toughness. This free interactive trainer lets you explore every region of the curve, study 15 key concepts with formulas and worked examples, and test your knowledge through practice problems and a quiz.
In the initial linear portion of the curve, Hooke's Law applies: stress is directly proportional to strain (σ = Eε). The slope of this line equals Young's Modulus (E), which measures the material's stiffness. Steel has E ≈ 200 GPa, while aluminium is about 70 GPa. The material returns to its original shape when the load is removed — this is elastic behaviour.
Beyond the elastic limit, the material begins to deform permanently. The yield stress (σy) marks this transition. For mild steel, a distinct upper and lower yield point is visible. After yielding, strain hardening strengthens the material until it reaches the Ultimate Tensile Stress (UTS) — the peak of the curve. Beyond UTS, necking occurs (a localised reduction in cross-section), and eventually the material fractures.
Ductile materials (mild steel, copper, aluminium) show a long plastic region with significant elongation before fracture. Brittle materials (cast iron, glass, ceramics) fracture suddenly with little or no plastic deformation — their stress-strain curve is nearly linear until a sharp break. Use the material toggle above to compare both curves side by side.
This trainer covers 15 essential concepts: Stress, Strain, Young's Modulus, Poisson's Ratio, Proportional Limit, Elastic Limit, Yield Stress, UTS, 0.2% Proof Stress, Necking, Factor of Safety, Resilience, Toughness, Ductile Material, and Brittle Material. Each concept includes a formula, units, description, and a worked example calculation.
Start in Learn mode to explore the stress-strain curve interactively — click regions to highlight them, drag the purple dot along the curve to read live σ and ε values, and toggle between ductile, brittle, and both views. Switch to Explore mode to study all 15 concepts with mini-diagrams and example calculations. Use Practice mode to solve random numeric problems (stress, strain, modulus, FoS calculations) with step-by-step solutions. Finally, take the Quiz — 5 mixed questions (MCQ + numeric) with a scored result panel.