Proof Stress

Many engineering materials, particularly ductile metals like aluminum alloys, copper alloys, and certain types of steel, do not exhibit the clear, sudden yielding behavior seen in mild steel. Their stress-strain curve transitions from elastic to plastic behavior gradually. For design and safety purposes, engineers need a consistent point to define the onset of permanent deformation. This is where proof stress, also known as offset yield strength, becomes crucial. To determine it, a tensile test is performed while plotting stress versus strain. A line is drawn on this graph parallel to the initial linear (elastic) portion of the curve, but offset from the origin by a specified strain value, most commonly 0.2% (or 0.002 strain). The stress at which this offset line intersects the stress-strain curve is defined as the 0.2% proof stress (\(\sigma_{0.2}\)).

This value is a practical and reproducible measure of the material’s elastic limit. It signifies that if the material is loaded to this stress level and then unloaded, it will have undergone a permanent deformation of 0.2%. While some plastic deformation has occurred, it is considered small enough to be acceptable for many structural applications. This convention allows engineers to design components using materials without a sharp yield point with the same safety and reliability principles as those with one, ensuring that structures do not permanently deform under their design loads.