The mechanical properties of solids are used to describe the solid’s strength, ability to deform, ability to withstand pressure, and resistance to change shape.
Here are the basic concepts that you need to know related to the mechanical properties of solids:
Deforming force
A force which, when applied, changes the shape or size of the solid.
Elasticity (reversible deformation)
The property of an elastic object by virtue of which it is able to regain its original shape once the deforming force is removed. For e.g. a rubber band.
A perfectly elastic body is an ideal concept. It is defined as an object which regains its original shape and size immediately after the removal of the deforming force. Quartz fibre and phosphor bronze are the only 2 materials which come close to being called perfectly elastic bodies.
Plasticity (irreversible deformation)
The opposite of elasticity, plasticity is the property of an object to completely and immediately lose its original configuration on the removal of a deforming force. E.g. an iron bar once heated will immediately lose its cuboidal shape.
A perfectly plastic body is also an ideal concept and is the one which does not regain its original configuration at all when the deforming force is removed. Paraffin wax and putty are nearly plastic bodies.
Stress
When force is applied to a body, an internal force of reaction comes into play per unit area of the cross-section of the body. This internal force is known as stress and is given by
Stress= External force/ Area
We use external force in the formula since the internal force that is set up is equal in magnitude but opposite in direction to the applied external one.
Unit of stress in SI system is N/(m^2) or Pascal, and in CGS system is dyne/(cm^2).
Types of stress:
- Normal or longitudinal stress – It acts perpendicular to the area of the cross-section of the body and is further divided into:
- Tensile stress – If the applied force leads to an increase in the length of the body, the stress is called tensile stress.
- Compressional stress- If the applied force leads to a decrease in the length of the body, the stress is called compressional stress.
- Tangential or shearing stress – It acts parallel to the area of the cross-section of the body.
- Hydraulic stress- The internal force set up in the body when the external force is applied by a fluid. Example – when a ball is submerged in water.
Strain
A dimensionless and unitless quantity, strain gives a measure of deformation of the body. It is of 3 types:
Longitudinal strain= change in length/ original length
Volumetric strain= change in volume/ original volume
Shear strain= small displacement, x/ original length, L
The shear strain measures the relative displacement between opposite faces of a body.
Elastic limit
The maximum stress below which the body can regain its original configuration on the application of force is called the elastic limit.
Hooke’s Law
The scientist Robert Hooke gave the Hooke’s Law. It states that within the elastic limit, the ratio of stress to strain is a constant. This ratio is known as the Modulus of Elasticity of the material. In other words, within the elastic limit, stress is directly proportional to strain.
Hooke’s law is applicable to all elastic bodies but not to plastic ones.
Mathematically,
Stress ∝ Strain
OR
F/A∝l/L
OR
Stress/ Strain= K
Where K is the Modulus of Elasticity.
Types of Modulus of Elasticity
All of them have N/(m^2) or Pa as their units. Within elastic limits, all of these are defined as:
Young’s Modulus
Given as
Y= longitudinal stress/ longitudinal strain
Metals generally have large Young’s Modulus. Greater the value of Y, greater the material’s elasticity.
Bulk Modulus
K= normal stress/ volumetric strain
The reciprocal of Bulk Modulus is known as compressibility.
C=1/K
Shear Modulus
G= shearing stress/ shearing strain
It is also called as Modulus of Rigidity.
For most materials, G=Y/3 i.e. Shear Modulus is less than Young’s Modulus.
Elastic after effect
The delay in regaining its original configuration by a material after the removal of deforming force is called elastic after effect.
Elastic fatigue
The altered elasticity of an elastic body due to repeated applications of the deforming force is called elastic fatigue.
Brittle materials
Materials which have a small range of plastic extension and break as soon as the elastic limit is reached are called brittle. E.g. glass.
Ductile materials
Materials which have a large range of plastic extension and can be drawn into wires are ductile materials. They show an irreversible increase in length before they break. E.g.- aluminium.
Elastomers
For elastomers, the strain produced is much greater than the stress applied within the elastic limit. E.g. rubber.
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