Yield stress vs proportional limit distinction

• A. The proportionality limit is where the yield stress occurs
• B. Yield stress is where noticeable permanent deformation begins; the proportionality limit is the linear region boundary
• C. They are the same point
• D. The yield stress is always less than the proportionality limit

Answer: (B)

The key idea is distinguishing elastic behavior from plastic behavior on the stress–strain curve. Up to the proportional limit, the material deforms elastically: stress and strain are proportional and all deformation is recoverable. The proportional limit marks the end of that linear region. Beyond this point, the material stops following Hooke’s law and plastic (permanent) deformation begins. The yield stress is the stress level at which noticeable permanent deformation starts to occur, defined in practice by criteria like the onset of plastic flow or a 0.2% offset criterion. So the yield stress is about the onset of yielding, while the proportional limit is simply the boundary of the linear elastic region. That’s why the statement describing yield stress as the point where permanent deformation begins and the proportional limit as the linear-region boundary is the best interpretation. The other options mix up these concepts or claim they are the same, which isn’t generally true.