Elastic Behavior of Solids

Dhristi JEE 2022-24

What is Elasticity?

Elasticity is defined as an attribute of rigid bodies to restore their original shape. Consider a spring hanging at one end through a rod at the top and the other end of it is left free. If I stretch this free end, the spring starts vibrating back and forth. It means the potential energy stored inside it transforms into kinetic energy; the spring is in solid form, so there is a tiny space between the successive atoms. Due to the force of attraction between them, they try to come back to their lattice points. This is how an interatomic force of attraction comes into play. So soon the stage comes when restoring force acting in the opposite direction to the applied force brings the spring into its natural state. Hence, the condition in which the body rolls back to its initial form. Such a condition is elasticity.


Explain Elastic Behaviour of Solids

Solid is one of the three states of matter composed of many molecules or atoms arranged in a particular form. Here, each molecule is acted upon by the forces because of neighbouring molecules.  The solids take such a shape that each molecule finds itself in a position of stable equilibrium. The rigid bodies when stretched with an external force restore their original shape after the removal of this force. It means they are in an elastic limit. So, until the elastic limit, the body resists the changes. Therefore, we can say that the body is perfectly elastic. Thus, the elastic behaviour of solids can be explained very well by observing the microscopic nature of the solids. 


Elastic Behavior of Solids

When a solid body is deformed, the atoms or molecules inside it are displaced from their fixed points or lattice points (equilibrium positions) causing a change in interatomic and intermolecular distances. When this force is removed, the interatomic force tries to bring back the body into its original position. Thus, the body comes to its original shape.


Mechanical Properties of Solids

The restoring mechanism can be visualized through a model of a spring ball system.  Here, the ball represents atoms and spring represents the interatomic force of attraction between the balls or atoms. 


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Initially, these atoms are in their respective lattice points as shown in Fig.2. When they are displaced from their points, the interatomic force of attraction brings the system to its original shape.


Deformation: The phenomenon of change in the shape of a body under the effect of applied force.


Deforming Force: The external force that is responsible for deformation in the shape of the system is called the deforming force.


Restoring Force: The opposite force that works in the way the frictional force does in a moving body. This force acts in the opposite direction, and it is a property of a body to come back to its original position after an external force is removed.


Physical and Chemical Properties of Solids

  • Solids are incompressible, which means that the constituent particles are placed close to each other, resulting in little space between the constituent particles.

  • Solids have a fixed mass, volume, and form, resulting in a compact arrangement of component particles.

  • Solids are inflexible. This is because there isn't enough space between the constituent particles, which causes it to be hard or fixed.

  • Molecules have a small intermolecular distance. As a result, the force between component particles (atoms, molecules, or ions) is extremely strong.

  • Particles in the system can only fluctuate about their mean locations.

  • The melting point of a solid is determined by the strength of the interactions between its constituents: stronger interactions result in a higher melting point.


Important Points on Elastic Behaviour of Solids


The attribute of a matter or a body under which a body regains its original configuration is called elasticity.  Let us understand this through an experiment:


On stretching a rubber band, we observe that there is a change in its shape and size. On releasing the band, the rubber regains its original length.


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The force applied to the rubber band is the deforming force. Therefore, the force that restores the elongated body to its original shape, and size is called the restoring force.


What Causes this to Happen?

Depending on their atomic elasticity, solids are formed up of atoms (or molecules). They are surrounded by other atoms of the same type, which are kept in balance by interatomic forces. When a force is applied to the solid, these particles are displaced, causing it to distort. When the deforming force is eliminated, the atoms revert to their previous state of equilibrium due to interatomic interactions. Because no substance is fully elastic, elasticity is an idealization.


Applications of Elastic Behavior of Materials

Elastic materials are those materials that can be used in places where the long-term usage of such material is required. The applications of elastic materials are outlined below:


  • Used in the construction of bridges, beams, columns, pillars: while constructing these materials, in-depth knowledge of the strength of the materials used in the construction is of prime importance.

  • Construction of cranes: Cranes are used to lift the loads. Therefore, great care is taken into consideration that the extension of the rope does not exceed the elastic limit of the rope.

  • In engineering, it is of utmost importance to know the elastic behaviour of materials being used.

  • The bridges are designed in such a way that they don’t get deformed or break under a load of heavy traffic, or due to the force of strongly blowing wind, and its weight.

  • Let’s consider a bar of length L and breadth d. Let Y be the young's modulus of the material of the bar. When a load ‘W’ is attached at its middle point, the depression δ produced at its middle point is given by,

                         δ = Wl3/4Ybd3

  • The metallic parts of the machinery are designed in such a way that when they are subjected to stress beyond the elastic limit, they will get permanently deformed.


Factors Affecting Elasticity

Effect of Stress: Even within the elastic limit, we know that when a solid is exposed to a high number of cycles of stresses, it loses its elastic characteristic. As a result, the material's operating stress should be kept lower than the ultimate tensile strength and the safety factor.


Effects of Temperature: Temperature affects the elastic properties of materials. Elasticity rises with lower temperatures and decreases with higher temperatures.


Effect Nature of Crystals: The flexibility of the crystals also relies on whether they are single crystals or polycrystals. The elasticity of a single crystal is higher, whereas the elasticity of a polycrystal is lower.


Effect of Annealing: Annealing is a procedure that involves heating a material to a very high temperature and then cooling it slowly. Typically, this technique is used to improve the material's softness and ductility. However, annealing a material causes the production of big crystal grains, which lowers the material's elastic properties.


Effect of Impurities: The presence of impurities causes variations in the materials' elastic properties. The type of impurity introduced to it determines how much elasticity it gains or loses.


Differences Between Elasticity and Plasticity

  • Elasticity is the quality of a solid material that allows it to restore its form once external stress is removed. Plasticity is the characteristic of a solid substance that allows it to keep its distorted shape even when the external load is removed.

  • The amount of elastic deformation is minimal. The amount of plastic distortion is substantial.

  • The amount of external force necessary to bend a solid elastically is relatively tiny. Plastic deformation needs a greater amount of force.

  • Within this elastic zone, Hooke's Law of Elasticity applies. If the material is plastically distorted, Hooke's Law does not apply.

  • Within this elastic area, most solid materials exhibit linear stress-strain behaviour. In the plastic zone, the stress-strain curve is non-linear.

  • Although atoms of the material are displaced from their original lattice location during elastic deformation, they return to their original position once external stress is eliminated. As a result, atoms are momentarily displaced. Plastic deformation causes solid atoms to be permanently displaced from their original lattice location. They maintain their new location even when the external stress is removed.

  • Elastic deformation takes place before plastic deformation. Only after it has been elastically deformed does it undergo plastic deformation.


The Similarity Between Elasticity and Plasticity

  • Both are the qualities of Solid.

  • Both forms of deformations can occur as a result of any sort of loading (normal, shear, or mixed).

  • Depending on the application, both elastic and plastic deformations might be advantageous.

  • Only when the material has been elastically deformed can plastic deformation begin. As a result, plastic deformation is impossible without elastic deformation.

FAQs on Elastic Behavior of Solids

1.What is Hooke’s Law of Elasticity?

Hooke’s law states that the extension produced in the wire is directly proportional to the load applied within the elastic limit. 

                          Extension  α  Load applied

We know within the elastic limit:

Stress α Strain 

Or,  

Stress  = E x Strain 

Where E is known as the modulus of elasticity of the body.

2.What is the formula for elasticity in physics?

According to the equation of Hooke’s law, F = kΔL, where ΔL is the amount of extension in the length of the material. So, elasticity is a measure of how difficult it is to stretch an object. In other words, it is a measure of how small the value of k is. The materials like rubber have a small k. Hence, they stretch a lot, even with a little force.

3.What are elastic stress and strain?

The stress acting on an object is directly proportional to the strain caused in the body within an elastic limit. It is represented as Stress α Strain.

4.Which is more elastic steel or rubber?

Steel is more elastic than the rubber because when it is stretched, steel regains its position earlier than rubber.

5.How can Vedantu help me understand the Chapter “Elastic Behavior of Solids.”?

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