Young’s Modulus of Elasticity Questions

One of the most important engineering tests is the bending or fracture of an object or material, and a characteristic showing that it has Young’s modulus of elasticity. Young’s modulus has been named after the English physicist Sir Thomas Young. The modulus describes the property of elasticity of a solid material that is undergoing tension or compression in a certain direction. It is the unchangeable fundamental property of a material. This is a measure of how easily the material will stretch or deform. In this article, we will get into the details of how to calculate Young’s modulus of elasticity and what to infer from the results provided.

Young’s modulus of elasticity

Young’s modulus can be defined as the property of a given material which can determine the point of its stretching and breaking. Young’s modulus of elasticity is defined as the ratio of tensile stress to tensile strain.

Tensile stress can be defined as the resistance of an object to an external force that could potentially tear it apart. The symbol of tensile stress is σ.

Tensile strain can be defined as the deformation or elongation of an object per unit length due to the application of tensile stress. The symbol depicts tensile strain = ϵ. Hence, Young’s modulus is denoted with the following expression:

E = σ/e,

where E denotes Young’s modulus

σ denotes tensile stress, and

ϵ denotes tensile strain

Definition of Young’s modulus

Young’s modulus of elasticity can be defined as the ratio of the amount of stress applied on an object to its level of resistance or elasticity to sustain the stress applied. Young’s modulus is also commonly referred to as the modulus of stress. 

For example, in the case of a metal rod, as heat is applied significantly on a metal rod, it elongates and stretches in due process, but once the heat is removed, it compresses to its original shape.

Factually, Young’s modulus describes how a material deforms under loading. We can take the example of the tensile test to further explain Young’s modulus of elasticity, note that with the actual conduction of the test, the stress-strain of the material is observed on a graph in the form of a curve. 

Young’s modulus formula  

Young’s modulus is also known as the modulus of elasticity. Young’s modulus of elasticity measures the stiffness of an elastic body. The higher the value of Young’s modulus, the stiffer the body becomes. 

In other words, the higher Young’s modulus, the less elastic the body or the object gets. The unit of Young’s modulus is N/m2. This is essentially the same unit as the unit of stress. 

Hence, Young’s modulus of elasticity is calculated as the ratio of stress to strain, and it is depicted with the following formula:

E =σ/e ,

where E denotes Young’s modulus

σ denotes tensile stress

and, ϵ denotes tensile strain

Now, since stress has the unit N/m2 and the strain has no unit whatsoever, Young’s modulus remains the same unit as stress.

Young’s modulus factors

In the case of elasticity of an object or material, the factors affecting Young’s modulus are as follows:

1. Stress: When a constant load or pressure is applied to the elastic material, it will cause the elasticity of the material to decrease or be reduced eventually.

2. Change in temperature: As the temperature of the material increases or decreases, it gradually affects the material’s elasticity. For instance, as the temperature of the material increases, it gradually starts becoming plastic in nature, i.e., it slowly leads towards deformation. However, a decrease in temperature will increase the elasticity.

3. Impurities: A material’s level of elasticity increases or decreases in nature, depending on the number of impurities added to it. For instance, as small quantities of alloys are added to iron, the elasticity of the iron increases gradually.

4. Hammering, rolling, and annealing: If an object or material is constantly hammered, the atomic bond of the particle breaks, eventually making it more elastic. A similar effect is depicted in the case of rolling and annealing of the material.

5. Crystalline nature: If the material is only crystalline, it cannot be considered an elastic property; hence, the lesser the material is crystalline, the more elastic it will be.

Rigidity Modulus 

• Shear modulus refers to the ratio of shear stress to the corresponding shear strain. Shear modulus is also called the Rigidity Modulus. 

The formula for Rigidity Modulus 

G represents the modulus of rigidity or shear modulus. 

Shear modulus formula: G = shearing stress / shearing strain

G= F/A / Δx/L

Shear Stress:

σs= F / A

And Shear Strain:

Θ =x / L

So, Rigidity Modulus can also be expressed as:

G=σs/ Δ

Or 

σS = G × Θ

The SI unit of shear modulus is  N/m2 or Pascal (Pa).

Conclusion

Young’s modulus of elasticity defines the elasticity rate of an object or material when constant stress is applied to the object. The modulus is depicted as the ratio of strain to stress.

Young’s modulus can be tested with tensile stress, where the load is applied to an object from a single direction to determine its elasticity level. Young’s modulus measures the stiffness of an elastic body; the higher the value of Young’s modulus, the stiffer the body becomes.