Physics · Mechanical Properties Of Solids · NEET
In your NCERT class 11 book they are treated as the same point B on the stress-strain curve. NCERT says: 'The point B in the curve is known as yield point (also known as elastic limit).' So for NEET, elastic limit = yield point = point B, and the stress at B is called yield strength (sigma_y). In advanced engineering they can differ slightly, but for NEET treat them as one point.
They are two different points and A comes before B. Up to the proportional limit (A), stress is directly proportional to strain, so Hooke's law holds and the graph is a straight line. From A to the elastic limit (B) the graph curves, so stress and strain are no longer proportional, BUT the body still returns to its original shape when the load is removed. So: proportional limit = end of straight line, elastic limit = end of elastic (recoverable) behaviour.
Once stress crosses the yield strength, strain increases very fast even for a small increase in stress (region B to D). If you remove the load here, the body does NOT return to its original length. Some strain stays even at zero stress. This leftover strain is called a permanent set and the deformation is called plastic deformation.
Hooke's law (stress proportional to strain) is only valid up to the proportional limit A. Between A and B the material is still elastic (it recovers), but the stress-strain relation becomes non-linear, so the straight-line rule of Hooke's law no longer applies. A common trap is thinking elastic behaviour and Hooke's law end at the same point. They do not: Hooke's law ends first (at A), elastic behaviour ends later (at B).
A permanent set is the strain that remains in a material even after the deforming force is completely removed, once it has been stressed beyond the yield point. If you unload at a point C between B and D, the material follows back a lower path and settles at a non-zero strain at zero stress. That non-zero strain is the permanent set, and the material is now permanently deformed.
The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus respectively are 8 x 10^8 N m^-2 and 2 x 10^11 N m^-2, is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The proportional limit is the point (A) up to which stress is directly proportional to strain. In this region the stress-strain graph is a straight line and Hooke's law is obeyed. Its slope gives the modulus of elasticity of the material.
Yield strength (sigma_y) is the value of stress at the yield point (point B), the maximum stress a material can take while still returning to its original shape. NCERT gives yield strength values for materials like mild steel (about 300 x 10^6 N m^-2), which are used in crane rope design.
Because the maximum safe stress or maximum elongation of a wire is set by the elastic limit. Many numericals ask for the largest elongation or the minimum thickness of a rope, and you use elastic limit or yield strength as the maximum allowed stress, then apply Y = stress / strain.
Elastic deformation is recoverable: the body returns to its original size and shape when the force is removed (below the elastic limit). Plastic deformation is permanent: the body keeps a permanent set even after the force is removed (above the yield point).
