The concept of proof stress was developed as a convention to determine and compare the yield strengths of different materials.

To understand this in detail, note that the yield point defines the onset of plastic deformation in materials. Since most metals obey the Hooke's law of linear elasticity, theoretically, the yield stress can be identified as the point after which the stress- strain curve deviates from linearity. Indeed, in some brittle or elastic-perfectly plastic materials, the stress-strain curve exhibits a distinct transition from linear elasticity to plasticity.

However, in most other metals and alloys it is non-trivial to determine this transition accurately as the stress-strain curve appears to be smooth and continuous. In such a condition, even magnifying the stress-strain curve and determining the subtle changes in its slope is not useful as local fluctuations can lead to incorrect and non-repeatable estimates of the yield point. Moreover, since some metals and alloys also have a non-linear elastic portion in their stress-strain response, such procedures are actively discouraged.

Therefore, the work-around solution to determine the yield point in such cases is to use to 0.2% proof stress method. The choice of 0.2% as the benchmark for proof stress is purely heuristic. It was previously determined--for alloys that exhibit a distinct yield point -- that a line drawn parallel to the linear portion of the stress-strain curve from 0.2% strain intersects the stress -strain curve at the yield point. This was subsequently used as a benchmark to compare the values of yield stress of other alloys that do not display a distinct yield point. Nevertheless, note that the actual theoretical yield stress may be slightly lower than the proof stress in many engineering alloys. However, given that most materials exhibit a high initial hardening rate near the proportionality limit, the proof stress convention is quite accurate.

In some materials, the stress at which the material changes from elastic to plastic behavior is not easily detected. In this case, the offset yield strength is determined. A line is constructed parallel to the initial portion of the stress-strain curve but offset by 0.002 in/in (0.2%) from the origin. The 0.2% offset yield strength is the stress at which the constructed line intersects the stress-strain curve.

The offset yield point (or proof stress) is the stress at which 0.2% plastic deformation occurs

The concept of proof stress was developed as a convention to determine and compare the yield strengths of different materials.

To understand this in detail, note that the yield point defines the onset of plastic deformation in materials. Since most metals obey the Hooke's law of linear elasticity, theoretically, the yield stress can be identified as the point after which the stress- strain curve deviates from linearity. Indeed, in some brittle or elastic-perfectly plastic materials, the stress-strain curve exhibits a distinct transition from linear elasticity to plasticity.

However, in most other metals and alloys it is non-trivial to determine this transition accurately as the stress-strain curve appears to be smooth and continuous. In such a condition, even magnifying the stress-strain curve and determining the subtle changes in its slope is not useful as local fluctuations can lead to incorrect and non-repeatable estimates of the yield point. Moreover, since some metals and alloys also have a non-linear elastic portion in their stress-strain response, such procedures are actively discouraged.

Therefore, the work-around solution to determine the yield point in such cases is to use to 0.2% proof stress method. The choice of 0.2% as the benchmark for proof stress is purely heuristic. It was previously determined--for alloys that exhibit a distinct yield point -- that a line drawn parallel to the linear portion of the stress-strain curve from 0.2% strain intersects the stress -strain curve at the yield point. This was subsequently used as a benchmark to compare the values of yield stress of other alloys that do not display a distinct yield point. Nevertheless, note that the actual theoretical yield stress may be slightly lower than the proof stress in many engineering alloys. However, given that most materials exhibit a high initial hardening rate near the proportionality limit, the proof stress convention is quite accurate.