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The ratio of change in configuration to the original configuration is called strain. Being the ratio of two like quantities, it has no dimensions and units. Strains are of three types:
Linear strain If the deforming force produces a change in length alone, the strain produced in the body is called linear strain or tensile strain (Fig. 3).
Fig. 3
Linear strain in the direction of deforming force is called longitudinal strain and in a direction perpendicular to force is called lateral strain.
Volumetric strain If the deforming force produces a change in volume alone, the strain produced in the body is called volumetric strain (Fig. 4).
Fig. 4
Shearing strain If the deforming force produces a change in the shape of the body without changing its volume, strain produced is called shearing strain (Fig. 5).
Fig. 5
It is defined as angle in radians through which a plane perpendicular to the fixed surface of the cubical body gets turned under the effect of tangential force.

Stress-Strain Curve

If by gradually increasing the load on a vertically suspended metal wire, a graph is plotted between stress (or load) and longitudinal strain (or elongation), we get the curve as shown in Fig. 6. From this curve, it is clear that:
Fig. 6
  • When the strain is small (< 2%) (i.e., in region OP), stress is proportional to strain. This is the region where the so-called Hooke’s law is obeyed. The point P is called limit of proportionality and slope of line OP gives the Young’s modulus Y of the material of the wire. Ifθ is the angle of OP from strain axis, then Y = tanθ .
  • If the strain is increased a little, i.e., in the region PE, the stress is not proportional to strain. However, the wire still regains its original length after the removal of stretching force. This behavior is shown up to point E known as elastic limit or yield point. The region OPE represents the elastic behavior of the material of wire.
  • If the wire is stretched beyond the elastic limit E, i.e., between EA, the strain increases much more rapidly and if the stretching force is removed, the wire does not come back to its natural length. Some permanent increase in length takes place.
  • If the stress is increased further, by a very small increase in it, a very large increase in strain is produced (region AB) and after reaching point B, the strain increases even if the wire is unloaded and ruptures at C. In the region BC the wire literally flows. The maximum stress corresponding to B after which the wire begins to flow and breaks is called breaking or tensile strength. The region EABC represents the plastic behavior of the material of wire.
    Stress–strain curve for different materials is shown in below.
Brittle material
Fig. 7
The plastic region between E and C is small for brittle material and it will break soon after the elastic limit is crossed.

Ductile material
Fig. 8
The material of the wire has a good plastic range and such materials can be easily changed into different shapes and can be drawn into thin wires.

Fig. 9
Stress–strain curve is not a straight line within the elastic limit for elastomers and strain produced is much larger than the stress applied. Such materials have no plastic range and the breaking point lies very close to elastic limit.
Example, rubber.

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