# Elasticity

Elastic Property of Matter:

(1) Elasticity: The property of matter by virtue of which a body tends to regain its original shape and size after the removal of deforming force is called elasticity.

(2) Plasticity: The property of matter by virtue of which it does not regain its original shape and size after the removal of deforming force is called plasticity.

(3) Perfectly elastic body: If on the removal of deforming forces the body regain its original configuration completely it is said to be perfectly elastic.

A quartz fibre and phosphor bronze (an alloy of copper containing 4% to 10% tin, 0.05% to 1% phosphorus) is the nearest approach to the perfectly elastic body.

(4) Perfectly plastic body: If the body does not have any tendency to recover its original configuration, on the removal of deforming force, it is said to be perfectly plastic.

Paraffin wax, wet clay are the nearest approach to the perfectly plastic body.

Practically there is no material which is either perfectly elastic or perfectly plastic and the behavior of actual bodies lies between the two extremes.

(5) Reason of elasticity: In a solids, atoms and molecules are arranged in such a way that each molecule is acted upon by the forces due to neighboring molecules. These forces are known as intermolecular forces.

For simplicity, the two molecules in their equilibrium positions (at inter-molecular distance r = r0) are shown by connecting them with a spring. In fact, the spring connecting the two molecules represents the inter-molecular force between them. On applying the deforming forces, the molecules either come closer or go far apart from each other and restoring forces are developed. When the deforming force is removed, these restoring forces bring the molecules of the solid to their respective equilibrium position (r = r0) and hence the body regains its original form.

(6) Elastic limit: Elastic bodies show their property of elasticity up to a certain value of deforming force. If we go on increasing the deforming force then a stage is reached when on removing the force, the body will not return to its original state. The maximum deforming force up to which a body retains its property of elasticity is called elastic limit of the material of body.

Elastic limit is the property of a body whereas elasticity is the property of material of the body.

(7) Elastic fatigue: The temporary loss of elastic properties because of the action of repeated alternating deforming force is called elastic fatigue.

It is due to this reason

⇒ Bridges are declared unsafe after a long time of their use.

⇒ Spring balances show wrong readings after they have been used for a long time.

⇒ We are able to break the wire by repeated bending.

(8) Elastic after effect: The time delay in which the substance regains its original condition after the removal of deforming force is called elastic after effect. It is the time for which restoring forces are present after the removal of the deforming force it is negligible for perfectly elastic substance, like quartz, phosphor bronze and large for glass fiber.

Stress: When a force is applied on a body there will be relative displacement of the particles and due to property of elasticity an internal restoring force is developed which tends to restore the body to its original state.

The internal restoring force acting per unit area of cross section of the deformed body is called stress.

At equilibrium, restoring force is equal in magnitude to external force, stress can therefore also be defined as external force per unit area on a body that tends to cause it to deform.

If external force F is applied on the area A of a body then,

Stress = Force/Area = F/A

Units: N/m2 (S.I.), dyne/cm2 (C.G.S.)

Dimension: [ML-1T-2]

Stress developed in a body depends upon how the external forces are applied over it.

On this basis there are two types of stresses: Normal and Shear or tangential stress

(1) Normal stress: Here the force is applied normal to the surface. It is again of two types: Longitudinal and Bulk or volume stress

(i) Longitudinal stress:

1. It occurs only in solids and comes in picture when one of the three dimensions viz. length, breadth, height is much greater than other two.
2. Deforming force is applied parallel to the length and causes increase in length.
3. Area taken for calculation of stress is area of cross section.
4. Longitudinal stress produced due to increase in length of a body under a deforming force is called tensile stress.
5. Longitudinal stress produced due to decrease in length of a body under a deforming force is called compressional stress.

(ii) Bulk or Volume stress:

1. It occurs in solids, liquids or gases.
2. In case of fluids only bulk stress can be found.
3. It produces change in volume and density, shape remaining same.
4. Deforming force is applied normal to surface at all points.
5. Area for calculation of stress is the complete surface area perpendicular to the applied forces.
6. It is equal to change in pressure because change in pressure is responsible for change in volume.

(2) Shear or tangential stress: It comes in picture when successive layers of solid move on each other i.e. when there is a relative displacement between various layers of solid. 1. Here deforming force is applied tangential to one of the faces.
2. Area for calculation is the area of the face on which force is applied.
3. It produces change in shape, volume remaining the same.
 Difference between Pressure and Stress Pressure Stress Pressure is always normal to the area. Stress can be normal or tangential. Always compressive in nature. May be compressive or tensile in nature.