## Mechanical Properties of Solids

Before Learning, the Mechanical Properties of Solids, what is Matter

The matter is broadly divided into three categories, viz. Solid, Liquid and Gas. Due to the strongest intermolecular force of attraction in solids, they are tough and have a definite shape and size. This force is relatively weak in liquids and so the shape is easily changed but liquids have a definite volume. In gases, the intermolecular force of attraction is minimum and hence, they do not have a definite shape, size, and volume. There is a fourth state of matter called plasma state in which matter exists in the ionized state. Plasma state is common in stars.

### Solids

In solids, the constituent particles (atoms, molecules or ions) are held strongly at the position of minimum potential energy. Solids are of two categories :

1. Crystalline Solids: They have a regular pattern of constituent particles in three-dimensional space. Hence, they have a definite external geometrical shape and a sharp melting point. They are an isotropic i.e. their physical properties like conductivity (thermal and electrical), refractive index, mechanical strength etc. have different values in different directions e.g. rice, sugar, quartz, diamond, rock salt, most of the metals & their compounds, etc.
2. Amorphous or Glassy Solids: They have an irregular arrangement of particles.
Hence, they do not have a definite external geometrical shape and sharp melting point. They are isotropic i.e. their physical properties have the same value in all directions e.g glass, cement, rubber, paraffin, plastic, etc.

### Elasticity of Solids

The property of the body by virtue of which it tends to regain its original shape and size after the removal of applied forces, is called elasticity and body itself is called elastic body.

Some Terms Related to Elasticity

• Deforming Force: The force which when applied changes the configuration of the body, is called deforming force.
• Perfect Elastic Body: A body which regains its original configuration immediately and completely after the removal of deforming force, is called perfectly elastic body e.g.., quartz, phosphor bronze.
• Plastic Body. A body which does not regain its original configuration at all on the removal of deforming force from it is called plastic body e.g., putty, mud, paraffin wax etc. The body that remains in deformed shape even after the removal of deforming force is called a perfectly plastic body.
• Elastic Limit. It is the upper limit of deforming force up to which, if deforming force is removed, the body regains its original form completely and beyond which, if deforming force is increased, the body loses its property of elasticity and gets deformed permanently.
• Elastic After Effect: The temporary delay in regaining the original configuration of an elastic body after the removal of a deforming force, is called elastic after effect.
• Elastic Fatigue. The property of an elastic body by virtue of which its behavior becomes less elastic under the action of repeated alternating deforming forces called elastic fatigue.
• Stress When a deforming force is applied on a body, it changes its configuration due to which an internal force comes into play which tends to bring the body back to its initial configuration.

The internal restoring force acting per unit area of a deformed body is called stress where σ is the stress, F is the force and A is the surface area.

Its unit is N/m² and dimensions are M1L1T-2

It is of two types

1. Normal Stress When a deforming force acts normally (perpendicularly) over the area of cross section of a body, then internal restroing force is called normal stress
2. Tangential or Shearing Stress. When a deforming force acts tangentially to the surface of the body and produces a change in the shape of the body, the stress surface of the body and produces a change in the shape of the body, the stress set up in the body is called tangential or shearing stress
• Strain. When a deforming force is applied on a body, there is a change in the configuration of the body. The body is said to a deformed.

The ratio of change is configuration to the original configuration, is called Strain is a ration of two similar quantities, so it has no units and dimesions.

It is of three types. Mechanical properties of solids

1. Longitudinal Strain. If there is a change in length alone due to deforming force then strain in the body is called longitudinal stra.
2. Volumetric Strain. If there is a change in volue due to deforming force, then strain in the body is called volumetric strain.
3. Shearing Strain. If the deforming force produces a chane in the shape of the body without changing its voluem, the strain is called shearing strain.

Thus, shearing strain is also defined as the ratio of displacement of a surface under a tangential force to the perpendicular distance of the displaced surface from the fixed surface

• Glass is more elastic than rubber because for a given applied force per uniit area, the strain produced in glass is much smaller than produced in rubber.
• Water is more elastic than air because the volume of elasticity is reciprocal of compressibility. Further, the air is more compressible than water Mechanical properties of solids

### Hooke’s Law (Modulus of Elasticity)

According to this law within the elastic limits, the stress is directly proportinal to the strain produced in a body

i.e. Stress ∝ Strain

or Stress = E x strain ⇒ Stress/Strain = E

Where E is constant of proportionality, it is called modulus of elasticity

Hooke’s law is valid only in the linear part of stress-strain curve.

There are three types of modulus of elasticity

#### Young’s Modulus of Elasticity (Y)

The ratio of longitudinal stress and longitudinal strain in the elastic limits, is called Young’s modulus

i.e.  Young’s Modulus = Longitudinal Stress/ Longitudinal Strain

#### Bulk Modulus of Elasticity (B)

The ration of normal stress to the volumetric strain within the elastic limits, is called bulk modulus of elasticity.

i.e. Bulk modulus = Normal stress / volumetric strain

Its SI units is N/m² or pascal and CGS units is dyne/cm²

The negative sign indicates the fact that twith an increase in pressure, a decrease in volume occurs.

Bulk modulus is involved in solids, liquids and gases. Bulk modulus for solids is much larger than that for liquids which is again much larger than the bulk modulus for gases Young’s modulus and bulk modulus for a perfectly rigid body is infinity.

#### Modulus of Rigidity or Shear Modulus of Elasticity (η)

The ratio of shearing stress to the shearing strain within the elastic limits, is called shear modulus of rigidity.
i.e.,    Modulus of rigidity (η) = Shearing Stress / Shearing Strain
Its SI units is N/m² or pascal and CGS unit is dyne/cm².

### Classification of Materials Based on the Property of Elasticity

Based on the property of elasticity, materials are classified as follows

#### Ductile Materials

The materials which show large plastic range beyond the elastic limit, are called ductile materials e.g., copper, silver, iron, aluminum, etc.
It is used for making springs and sheets

#### Brittle Materials

The materials which show very small range beyond the elastic limit, are called brittle materials, e.g., glass, cast iron, etc. Mechanical properties of solids

#### Elastomers

The materials for which strain produced is much larger than the stress applied within the limit of elasticity, are called elastomers. e.g., rubber, the large vessel carrying blood from the heart, etc.
Elastomers have no plastic range.