## Young’s modulus

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 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 denotes the tensile stress = 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 the tensile strain= ϵ

Hence, Young’s modulus is denoted with the following expression:

E =

Where,

E denotes Young’s modulus

σ denotes tensile stress

and, ϵ denotes tensile strain

## Define Young’s modulus

Young’s modulus 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.

The 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.

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, 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. Where strain is depicted on the x-axis and stress is depicted on the y-axis:

- The tensile test is a very common mechanical test that takes a test piece and stretches it along its length.
- It is a uniaxial test which means that it applies the force of the solid object from only one direction.
- During the test, the test machine measures the applied load or force on the solid object and the change in length of the same.
- The main output from the tensile test is the stress-strain curve, which describes how much the object or the material we are testing will deform for different levels of applied stress.
- While conducting the test, we can observe how the stress-strain curve evolves the material or the object we are conducting the test on; ideally, we can use any metal solid such as steel.
- The test comes to an end as the metal fractures or breaks down eventually.

By the example of the tensile test, we can observe that the stress-strain curve is split into two regions

The elastic region where we can observe that the curve is linear (in this region, the stress is greater than the strain on the graph)

The plastic region (where the strain is greater than the stress on the graph).

Suppose the applied stress is low and we remain in the elastic region. In that case, the original dimensions of the component will be completely recovered when the applied force or load is removed. For larger stresses that take us into the plastic region, permanent plastic deformation will remain after removing the applied load.

### Young’s modulus formula

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

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 is as follows:

- 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.

- 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.

- Impurities- In terms of the number of impurities added to the material, its level of elasticity increases or decreases in nature. For instance, as small quantities of alloys are added to iron, the elasticity of the iron increases gradually.

- Hammering, rolling, and annealing (which means heating a material and then cooling it gradually) – 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.

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

### Conclusion

Young’s modulus, which is named after the English Physicist- Sir Thomas Young, defines the elasticity rate of an object or material as constant stress is applied on 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.