Q.Sketch (in words) the shape of the stress-strain curve for a ductile metal such as mild steel as it is loaded from zero stress until it finally breaks. Identify and describe, in the order they occur, the proportional limit, the elastic limit, the yield point, the point of ultimate tensile strength, and the fracture point, and state briefly what physically distinguishes the elastic and plastic regions of the curve.

For a ductile metal such as mild steel, loaded steadily from zero stress until it finally breaks, the stress-strain curve passes through the following landmarks, in order:

1. Proportional limit ($P$): the curve is a straight line from the origin up to this point -- Hooke's law holds exactly here, and the line's slope equals Young's modulus $Y$.
2. Elastic limit ($E$): just beyond $P$, very close to it for most metals -- the last point up to which the material still returns completely to its original length if the load is removed, even though the curve is no longer perfectly straight between $P$ and $E$.
3. Yield point ($Y$): shortly beyond $E$, the curve flattens sharply -- the material now stretches a comparatively large amount for only a very small further increase in stress. This marks the start of the plastic region: if the load were removed anywhere past this point, the specimen would be left permanently longer than before.
4. Ultimate tensile strength ($U$): as loading continues through the plastic region, the stress needed to keep deforming the material rises to a maximum -- the highest stress the material can bear -- after which the specimen begins to visibly thin ("neck") at one point along its length.
5. Fracture point ($F$): once necking begins, the curve actually turns downward (less overall force is needed to keep stretching the now-thinner neck), until the wire finally snaps at $F$. …

Trace the stress-strain curve of a ductile metal in the order stress increases, naming each landmark point and stating, for each region between landmarks, whether the deformatio …

• Placing the yield point before the elastic limit, rather than after it -- the order is proportional limit, then elastic limit, then yield point. …