Mechanical Properties of Solids | Physics Class 11 - NEET PDF Download

Till now we have learned that solids have fixed shapes and dimensions i.e. they are rigid. You must have observed that if a weight is hung from the end of a vertically hung steel spring, it gets stretched. When the weight is removed, it goes back to its original shape and size. This shows that steel spring has some elastic behavior!

Stretching of Springs

In this document, we will be studying the Elasticity of solids in detail.  

Elastic Behaviour of Solids

The property of the body to regain its original configuration (length, volume, or shape) when the deforming forces are removed, is called elasticity.

Spring-ball model for the illustration of elastic behavior of solids

• In a solid, atoms and molecules are arranged in such a way that each molecule is acted upon by the forces due to the neighboring molecules. These forces are known as intermolecular forces.  For instance, assume the atoms or molecules of solid as the balls in the image below and the springs represent the interatomic or intermolecular forces. This is called the spring-ball model of solids.
• In this system, if any ball is displaced from its equilibrium position, the ball attached to it will be stretched or compressed. Due to this, restoring forces will come into play and force the ball to come back to its original position. This leads to elastic behavior in solids. 
• The change in the shape or size of a body when external forces act on it is determined by the forces between its atoms or molecules. These short-range atomic forces are called elastic forces.

Terms Related to Elasticity

1. Deforming force 

A force that when applied changes the normal position of the molecules thus resulting in the change of configuration of the body.

2. Elastic body

A body that regains its original configuration immediately and completely after the removal of deforming force from it is called a perfectly elastic body. Quartz and phosphorus bronze are examples of nearly perfectly elastic bodies.

Elastic Materials

3. Plastic body
The inability of a body to return to its original size and shape even on removal of the deforming force is called plasticity and such a body is called a plastic body.

Plastic Materials

Stress

Stress is defined as the ratio of the internal force F, produced when the substance is deformed, to the area A over which this force acts.

In equilibrium, this force is equal in magnitude to the externally applied force. In other words,

The SI Unit of stress is newton per square meter (Nm^-2).In CGS units, stress is measured in dyne cm^-2. The dimensional formula of stress is ML^-1T^-2 

Stress is of two types:

Tensile and compressive stress

2. Tangential stress: When the elastic restoring force or deforming force acts parallel to the surface area, the stress is called tangential stress or shear stress.

Tangential Stress

Strain

It is defined as the ratio of the change in size or shape to the original size or shape. It has no dimensions, it is just a number.

Strain is of three types:

1. Longitudinal strain: If the deforming force produces a change in length alone, the strain produced in the body is called longitudinal strain or tensile strain.
It is given as:

Longitudinal strain

2. Volumetric strain: If the deforming force produces a change in volume alone, the strain produced in the body is called volumetric strain. It is given as:

Volumetric strain3. Shear strain: The angle tilt caused in the body due to tangential stress expressed is called shear strain. It is given as:

Shear strain

The maximum stress to which the body can regain its original status on the removal of the deforming force is called the elastic limit.

Hooke’s Law

Hooke’s law states that, within elastic limits, the ratio of stress to the corresponding strain produced is a constant.

This constant is called the modulus of elasticity. Thus,

Stress-Strain Curve

Stress-strain curves are useful to understand the tensile strength of a given material. The given figure shows a stress-strain curve of a given metal.

Stress-strain curve

• The curve from O to A is linear. In this region, Hooke’s Proportional limit law is obeyed.
• In the region from A to B stress and strain are not proportional. Still, the body regains its original dimension, once the load is removed.
• Point B in the curve is the yield point or elastic limit and the corresponding stress is known as yield strength of the material.
• The curve beyond B shows the region of plastic deformation.
• The point D on the curve shows the tensile strength of the material. Beyond this point, additional strain leads to fracture, in the given material.

Summary

• Elasticity is a measure of the deformation of an object when a force is applied. Objects that are very elastic like rubber have high elasticity and stretch easily.
• Stress is force over an area.
• Strain is the change in length over the original length.
• Most objects behave elastically for small strains and return to their original shape after being bent.
• If the strain on an object is greater than the elastic limit of the object, it will permanently deform or eventually fracture. Fracture strength is a measure of the force needed to break an object.