Mechanical Properties of Solids

A rigid body seems to have a specific shape and size. But in reality, a rigid body can be compressed, elongated, or even bent. The suitable operation which can be carried out on a body depends upon its mechanical properties.

Thus it can be concluded that rigid bodies can be deformed. The behaviour of a rigid body depends on the different mechanical properties such as stress, strain, elastic modulus, plasticity, etc.

The mechanical properties of solids play a vital role in material selection in design engineering. An engineer selects a particular material based on the application. If the application involves a high-stress situation, such as a piston in an engine, then a material of high strength (such as aluminium) is selected so that it can withstand high stress without breaking.

This article will provide you with explanations related to the different mechanical properties of solids and the different mechanical properties of solids formulas.

Stress and Strain

Stress and strain are the two fundamental mechanical properties of solids. Once you understand stress and strain, you can easily understand the different mechanical properties of solids. 

Stress is defined as the force acting per unit area. When an external force is applied to the body, the body undergoes deformation. To restrict this deformation, an internal resisting force is developed in the body, and the resisting force acting per unit area of the body is called stress. Stresses can be of different types, such as tensile stress, compressive stress, and shear stress. The formula for stress is as follows:-

σ=F/A

In the above-mentioned formula,

F = external force applied to the body 

σ = stress induced in the body 

A = cross-section area of the body

Strain is the by-product of stress. When an external force is applied to the body, the body undergoes deformation. Due to the deformation of the body, the dimensions of the body change. Hence the ratio of change in dimension to the original dimension is called strain. Strain can be of different types: longitudinal strain, lateral strain, shear strain, and volumetric strain.

Elasticity and Plasticity

When an external force is applied to the body, the body undergoes deformation. But suppose that the body retains its original shape when the force is removed. In that case, the body is said to be elastic. This property of gaining the original shape after removing the force is referred to as elasticity. An example of an elastic body is a spring.

Plasticity is the opposite of elasticity. Therefore, when a force is applied to the body, such that it doesn’t regain its original shape after the removal of the force, then it is known as plasticity. If an elastic body enters the plastic region, it expands to the point until its failure.

Modulus of Elasticity or elastic moduli

Elastic modulus is the ratio of tensile stress to the longitudinal strain. Elastic modulus is denoted by “Y.” Elastic modulus is not a dimensionless quantity. Its dimension is similar to the dimension of stress. The formula for Young’s modulus is as follows:-

Y=Tensile or compressive stress/Tensile or compressive strain

The value of Young’s modulus is different for every material. If the value of Young’s modulus for a certain material is high, it takes more force to deform the material by a small length. For example, to change the length of a steel wire, a force of 2000N is required, while to change the length of metals such as aluminium, brass, and copper wire, you need to apply forces of 690N, 900N, and 1100N. Therefore, it is clear that steel is more elastic, and due to its elasticity, steel is used in different structures and heavy machines.

Shear Modulus

Shear modulus is defined as the ratio of shear stress to the corresponding shearing strain. The shear modulus is generally represented by the letter G, and it is also known as the modulus of rigidity. Another thing you will notice with the shear modulus is that its value is much lower than the value of the elasticity modulus. For many materials, the value of shear modulus is 1/3 of the value of elasticity modulus. The formula for shear modulus is as follows:-

G=shearing stress/Shearing strain

Here is the value of shear modulus for some common elements:

Aluminium – 25 GPa

Brass – 36 GPa

Copper – 42 GPa.

Bulk Modulus

Bulk modulus is one of those mechanical properties of solids that act on the body when submerged in a liquid. When a body is submerged in a liquid, it experiences stress. The stress developed on the body leads to a decrease in the volume of the body that in turn produces a strain in the body known as the volumetric strain. Thus the bulk modulus of a body is defined as the ratio of hydraulic stress to the corresponding hydraulic strain. Bulk modulus is defined by the letter ‘B.’ The formula for bulk modulus is as follows: –

B=-p(∆vv)

Here, the negative sign depicts that with the increase in pressure, the volume of the object decreases. The SI unit of Bulk modulus is similar to the unit of pressure.

Conclusion

Understanding the mechanical properties of solids is essential for understanding the behaviour of the material under different conditions. This article gives you vital information about mechanical properties such as the Bulk modulus, Shear modulus, Elastic modulus, and Stress and strain. Besides explaining the definition of the different mechanical properties, insights are also provided about how their values affect the material’s behaviour. It is important to know the different mechanical properties of solids before selecting a material for a particular application.