Stress-Strain Diagram:

1. Proportional Limit (P):

• From the figure (a), it is seen that the stress-strain relationship is linear from point O to point P i.e OP is a straight line. Hooke's law which states that the stress is directly proportional to strain, holds good only up to point P. Beyond point P, the curves deviate from the straight line. The point P is called the proportional limit.
  • Thus proportional limit is a point at which the stress-strain curve first begins to deviate from a straight line.
  • Hence, up to at which first begins from a straight line.

Hence, up to propotional limit,

$\sigma \ \alpha \ e$

$\sigma = E \ e$

or $E=\frac{\sigma}{e}$

where,

$\sigma$ = stress, $N/mm^2$

$e = strain$

$E = \text{modulus of elasticity}$, $N/mm^2$

2. Elastic Limit (E):

• Even if the material is stressed beyond point P and upto point E, it will regain its original size and shape when the load is removed. Thus, the material is in elastic range upto point E. This point E is called the elastic limit.
• The elastic limit is a point till which the material exhibits the eleastic properties.

3. Yield Point $(Y_1,Y_2,Y)$:

• If the material is stresses beyond point E, the plastic deformation takes place and the material starts yielding i.e. it will not regain its original size and shape even after the removal of load.
• Beyond point E, the strain increases at a faster rate upto point $Y_1$. At point $Y_1$, there is an appreciable increase in strain without increase in stress. In case of the mild steel, it is observed that there is a small reduction in stress and the curve drops down to point $Y_2$.
• The points $Y_1$ and $Y_2$ are called upper and lower yield points respectively. For many materials, the point $Y_1$ and $Y_2$ are very close to each other and difficult to distinguish. In such cases, for all practical purposes the two points are considered as same and is called yield point, Y. The stress corresponding to yield point is called yield strength, $S_Y$
• The yield strength is defined as the stress at which strain (or elongation) increases without increase in stress (or load)
• Many non-ferrous materials, heat treated steels, and brittle materials do not have a well defined yield point. For such materials, the yield strength can be evaluated as the stress at which the material show a specified derivation (normally 0.2%) from the linear stress-strain curve. This method is known as offset-method.
• In this method, a specified offset (normally 0.2%) is laid off along the strain axis. (i.e. OA = 0.002), as shown in fig.(b). A line is then drawn through point A, parallel to OP, and intersection of this line with stress-strain curve is called Yield Point Y and the corresponding stress is called 0.2% yield strength.

4. Ultimate strength (U):

• Beyond yield point, the plastic deformation of material increases and stress increases with strain till point U. At point U, the stress is at its maximum value and is referred as ultimate strength, $S_u$.
• The ultimate tensile strength is the maximum stress that can be reached in a tensile test.

5. Breaking strength (F):

• In a ductile materials, the cross-sectional area of the specimen decreases rapidly beyond point U. This leads to the formation of neck and subsequent fracture at the narrowest cross-section of the neck. The stress corresponding to point F is called breaking strength or fracture strength.