Yield strength is the stress at which permanent deformation begins, ultimate tensile strength is the maximum engineering stress a material withstands, and the fracture point is where the material finally breaks. They are distinct positions on a tensile stress-strain curve.
Reading the Stress-Strain Curve
During a tensile test, an increasing tensile force is applied to a specimen. Engineering stress is calculated using the original cross-sectional area:
where is tensile force and is the original cross-sectional area. Engineering strain is , where is the extension and is the original length.
Initially, the material undergoes elastic deformation: it returns to its original dimensions when unloaded. At the yield strength, significant plastic deformation begins, so unloading leaves permanent extension.
| Property | Position and meaning | Design significance |
|---|---|---|
| Yield strength | Stress at the transition from elastic to plastic behaviour | Often used to determine a safe working stress because structural components should not deform permanently |
| Ultimate tensile strength | Highest point on the engineering stress-strain curve | Represents the maximum engineering stress reached before localized narrowing usually develops |
| Fracture point | Final point, where the specimen separates | Identifies the engineering stress and strain at complete failure |
For a typical ductile metal, necking begins around the ultimate tensile strength. The specimen's cross-sectional area then decreases locally, and the engineering stress may fall before fracture because it is still calculated using . The order is therefore usually: yield strength, ultimate tensile strength, then fracture point.
A common misconception is that ultimate tensile strength is always the stress at which the material breaks. For a ductile material, fracture normally occurs later and at a lower engineering stress; brittle materials may fracture with little or no plastic deformation.
IB Exam Technique
For A3.2 structural systems, label these three points accurately on a stress-strain curve and explain their design implications. Do not confuse strength with stiffness: stiffness is indicated by the gradient of the elastic region, not by the yield or ultimate strength.