# Chapter 9 – Mechanical Properties of Solids

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Though solids are often associated with rigidity, in reality, solids exhibit many more qualities such as stretching, compression, elasticity, among others. You might have seen a metal rod being bent, stretched, and compressed with an external force while watching a blacksmith at work. Now, a solid being bent or stretched is not a miracle. Solids change shape when external deforming forces act on it. A solid has a definite shape and size that can be deformed only when external forces act on it; the characteristic property which enables solids to remain rigid are the mechanical properties of solids. Take a look at the properties of solids below:

1. Elasticity
2. Stress
3. Strain
4. Hooke’s law
5. Stress-strain curve
6. Elastic moduli

#### Elastic behavior of solids

Let’s try to understand what elasticity is.

Elasticity is one of the mechanical properties of solids by virtue, via which the solid material regains its original shape and size after the exposure of the external deforming force. Elastic behavior of solids is the resistance offered by the solids to prevent any permanent changes in the material after external stress.

For example, a rubber band shows elasticity when stretched. When stretched to a certain extent, the rubber band always returns to its shape and size.

Elasticity is different from plasticity. Whenever we apply external force/stress to a solid, it shows elasticity. If the solid fails to regain its original size after the application of non-reversible external force, it shows plasticity. Plasticity is the tendency of a solid to exhibit a non-reversible change after the removal of deforming force.

Take the previous example; as long as the rubber band stretched to a certain extent, it regained its original shape and size. Once it is stretched above that point, it starts losing its shape. The point till it stretches and regains shape is elasticity; the point beyond which a solid fails to regain original shape is plasticity.

An example of an almost perfect-elastic solid is quartz fiber.

An example of the nearest perfect-plastic solid is putty or paraffin.

#### Stress and strain

When you apply an external force on a cross-section of a solid, it produces an internal resisting force to prevent the solid from a permanent change. Stress is the ratio of internal force when the solid is deformed and the cross-section area of the solid onto which the force acts. Look at the formula below

The magnitude of the stress = F/A,

where F = internal force applied;

A= Area of the solid.

The SI unit of stress is Nm2 or Pascal (Pa). The dimensional formula of stress is [ML–1 T–2]. Stress is of two types as listed below.

1. Normal stress: It is the restoring force per unit area that you apply perpendicular to the surface of the body. Tensile stress and compressive stress are types of normal stress.
2. Tangential stress: When you apply elastic restoring force/deforming force parallel to the surface area of the solid, the resulting stress is tangential stress.

The strain is a change in the size or shape of a solid to the original size or shape. The strain is a dimensionless and unitless property.

Strain = change in the dimension of the solid/original dimension of the solid.

Longitudinal strain: A solid is under longitudinal strain when the deforming force acts to produce change only in length. The longitudinal strain is also called tensile strain. Imagine a long metal rod. When the external forces act on it, the type of strain produced is longitudinal, along the length of the solid.

Longitudinal strain

Here, the numerator L is the change in the length of the body. Denominator L is the original length of the body.

Volume strain:  A solid is under volume strain when you apply deforming force acts to produce a change in its volume. Let’s take a metal sphere, for example, here. When the forces act on it, the totality of strain is on the volume of a sphere. Due to its shape, when it expands, the volume of the sphere increases and vice-versa.

Volume strain

Here, the numerator V represents the change in the volume due to deformation. Denominator V is the original volume.

Shear strain: The tilt in angle caused in a body when you apply tangential stress is called shear strain. Shearing strain is expressed in terms of angle. A classic example of shear strain is when you press a book from the top; instead of compressing, it tilts slightly sidewards.

Shearing strain

Here x = relative displacement of the faces of the body

L= length of the body

#### Hooke’s law

When only a small deforming force acts on a solid, the resulting stress and strain are proportional to each other. This is known as Hooke’s law.  In other words, the ratio of stress and strain of a solid produces a constant known as modulus of elasticity.

Formula for Modulus of elasticity (k) = Stress/ Strain

Since strain is unitless, the modulus of elasticity shares its dimensions with stress. Nm-2

Hooke’s law of elasticity was discovered by Robert Hooke, an English scientist.

#### Stress-strain curve

The stress-strain curve shown above is a typical example of metal. It’s necessary to analyze the tensile strength of a body. In the curve, various behaviors shown by metal are displayed. Let’s discuss these behaviors one by one.
From point O to A, the metal exhibits Hooke’s law of elasticity, and A is the proportional limit.
B is the point of elastic limit; this is the maximum point where the solid metal regains its original shape back.
Point C onwards, the solids behave in a plastic manner. They cannot retrieve the original shape and size anymore.

At point E, the solid breaks; hence it is known as fracture limit.

Elastic moduli

The ratio of stress and strain is known as the modulus of elasticity or elastic moduli. It is considered a characteristic property of a material. Mentioned below are some moduli. Let’s go through them.

Young’s modulus

It is given as

Young’s modulus (Y)= Longitudinal stress/Longitudinal strain

Among solids, metals exhibit larger Young’s modulus. With an increase in Young’s modulus, elasticity increases.

Bulk modulus

It is expressed as

Bulk modulus (K) = Normal stress/Volume strain

It describes the elastic properties of solids when under pressure in all directions.

Shear modulus

It is given as

Shear modulus (G)= Shearing stress/shearing strain

It is also known as the modulus of rigidity.

#### Applications of elastic behavior of materials

The knowledge and applications of elastic behaviour are of great importance in everyday life. Some of them are listed below:

1. While designing a building, the structural design requires knowledge of the elasticity of solid materials.
2. The designing of any bridge needs to withstand the weight, weather, and ruins of traffic.

1. What are the mechanical properties of materials?

Answer. Mechanical properties of materials define the way they react when subjected to an external force. Whether a material is elastic/rigid or somewhere in between is determined by the mechanical properties.

2. What are the mechanical properties of solids?

Answer. Mechanical properties of solids include elasticity, brittleness, bulk modulus, shear strength, stress, strain, and many more.

3. How do you measure mechanical properties?

Answer. Mechanical properties are measured using the elasticity, stress-strain curve, and bulk modulus.

4. What are the five properties of materials?

Answer. The specific properties of materials include hardness, density, elasticity, ductility (or malleability), and conductivity.

Mechanical properties of solids are the reason why they can be twisted, turned, bent, and stretched. This session explained the basics of mechanical properties, to learn about the formulas of elastic moduli, stress-strain curve, and Hooke’s law divert a little of your attention to the latest online learning platform, MSVgo application.

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