Stress Vs Strain

In Physics, forces that describe the deformation of objects are called stress and strain. The force acting per unit area of a body is called stress, whereas the result of stress on a body or the deformation caused by the stress on the material is called strain. Thus there is a direct relationship between stress and strain, which are also deforming forces.

What is stress?

When there is an application of an external deforming force on a body, the body gets deformed. However, the body itself applies an opposite force to get back to its original size and shape. This force is generally produced from within the body.

This force that is generated within the body is usually equal in magnitude to the deforming force, but opposite in direction. Hence, stress can be termed as the restoring force produced per unit area of the body.

Properties of Stress

• Stress is a tensor quantity
• The symbol σ denotes stress 
• The measurement of stress is done in Pascal or N/m2

Formula for Stress

The formula for stress is:

                    σ=F/A

where

F= restoring force in Newton

A= cross-sectional area in m².

σ = it is the stress in N/m²

Types of Stress

The two main types of stress are normal stress and shearing or tangential stress. These are further divided into other types.

1.Normal Stress

Stress is called normal when the external force acts in normal (perpendicular) to the body’s cross-sectional area. This stress can be further divided into two types:

• Longitudinal stress
• Volumetric or bulk stress
• Longitudinal stress – In longitudinal stress, the external force acts along the length of the body. Hence, the main change occurs in the length of the body and there is only a slight change in the diameter of the material. It can be further divided into two types:

Tensile stress – It results in the increase of the body’s length.

Compressive stress – It is due to the decrease in the length of the body.

• Volumetric or bulk stress – When the deforming force acting on a body causes a change in its volume, it is called volume or bulk stress.

 2. Tangential or Shearing Stress

When the external force acts on the body in parallel to the cross-sectional area, then the stress is said to be tangential or shearing stress.

What is strain in Physics?

Strain is the measure of deformation caused to a body due to stress. We can also say that it is a measure of the physical change that occurs in a body due to the application of stress.

Strain is a unitless quantity as it is a ratio and the numerator and denominator in the fraction have the same units. Hence, the units get cancelled. There are the following three types of strain:

Normal Strain

Normal strain is also called longitudinal strain. It is the change in length of the body to the original length. Normal strain can be calculated by finding the ratio of change in length and the original length of the body.

Shearing Strain

Shearing strain is the angular deformation generated in a body. It is the ratio of the displacement of the body’s surface to the height of the body. 

Bulk strain or volumetric strain

It is the ratio of the change in volume of the body and the original volume of the body.

Formula of Strain

Strain (ε)= Δx/X

where,

ε is strain

Δx is a change in the dimensions

X is the original dimension

Stress and strain relationship

The relationship between stress and strain is directly proportional. However, it is directly proportional only up to the elastic limit. The stress and strain relationship can be better explained with the help of Hooke’s law. According to Hooke’s law, the strain is directly proportional to the stress applied to a solid up to the solid’s elastic limit. 

Stress vs strain graph

The relationship between stress and strain can be understood in a better way through the stress vs strain graph. 

• Proportional limit – The region of the graph that observes Hooke’s law is called the proportional limit. 

• Elastic limit – It is the highest amount of stress tolerated by a body before the occurrence of permanent deformation. It means that stress more than the elastic limit of the body will change its shape and size permanently.

• Yield point – The point after which the material starts getting deformed plastically is called the yield point. 

• Ultimate strength – This is the point of highest endurance of stress by the body. Any more stress after this point will break the body.

• Breaking point or fracture point – Applying stress on the body till this point finally breaks down the body. Hence, this point is called a fracture or breaking point.

Conclusion

Stress and strain are the forces used to describe deformation in a body. Stress is the restoring force that acts on the body in response to the external deforming force applied to the body. It is of mainly two types which are further divided into more kinds. Strain is the result of stress on the body. Strain is a unitless quantity as it is a ratio. Moreover, strain is also classified into three types which are- normal, shearing, and volumetric strain. Furthermore, the stress and strain relationship is directly proportional and is explained with the help of Hooke’s law.  The stress vs strain graph explains the relationship between stress vs strain in an elaborate manner.