Yield strength is the stress level at which a material begins to deform plastically, meaning that beyond this point, deformation is permanent and the material will not return to its original shape when the load is removed. It marks the end of the elastic region and the beginning of the plastic region on a stress-strain diagram.
For many ductile materials, particularly metals, the transition from elastic to plastic deformation is gradual, making it difficult to define an exact yield point. To address this, engineers often use the 0.2% offset yield strength, which is determined by drawing a line parallel to the elastic portion of the stress-strain curve, offset by 0.002 (0.2%) strain. The intersection of this line with the curve defines the yield strength, ensuring a consistent measurement even for materials with no clear yield point.
In materials that do not exhibit a well-defined yield strength, such as some aluminum alloys and polymers, an alternative measure called proof stress is used. This is similar to the 0.2% offset yield strength, but the offset strain may vary depending on the material and standard specifications.
Yield strength is a critical property in engineering design because it determines the maximum stress a material can handle without permanent deformation. Structural components, fasteners, and load-bearing materials are designed to operate well below their yield strength to maintain integrity and avoid plastic deformation, which could compromise function and lead to failure over time.
Constructing the .2% Offset Yield Line
If we start with the elastic line for a material, its equation in the stress–strain plane is
σ = E·ε
where
σ = stress
ε = strain
E = Young’s modulus (slope of the line)
This line passes through the origin and represents ideal linear elastic behavior.
To construct the 0.2% offset line, we keep the same slope E but shift the line to the right by 0.2% strain, which is
0.2% = 0.002 (as a decimal strain)
A horizontal shift of a linear function to the right by 0.002 is done by replacing ε with (ε − 0.002).
So the new equation becomes
σ = E·(ε − 0.002)
That is the mathematical form of the 0.2% offset line.
