# Thermal Stress

## What is Thermal Stress?

The meaning of the word ‘thermal’ is ‘temperature’. So, the stress which is produced as the result of temperature variation is what we call thermal stress.

More simply, we define thermal stress as the restoring force per unit area which is produced when a temperature change deforms a body or material. As thermal stress is an outcome of a change in temperature thus, the higher the temperature change more will be the more stress produced.

Now, before discussing more theories of thermal stress.

### What is Stress?

Hans Selye, in the year 1936, coined the term ‘stress’.

Selye was a person of American Origin. He was known as the ‘father of stress research’.

Stress is the restoring force acting per unit area of a material.

Now, I think you must have a question – how restoring force came into action?

So, when an external force is applied to an object, then it undergoes some amount of deformation, which can be large or small according to the material from which it is composed. It is not necessary that one can always visually notice the deformation when force is applied, but it is there even when not visible clearly.

So, when the deforming force acts on an object, then the object develops a restoring force of equal magnitude but in the opposite direction to that applied force.

This restoring force of the body per unit area is the stress. And when the deformation applied is the result of the change in temperature, then the generated restoring force per unit area is the thermal stress.

### Formula

Consider that F represents the applied deforming force and A is the cross-sectional area of the object. Then the magnitude of stress will be given as: As here we have said that change in temperature is deforming the object thus, the thermal stress will be the ratio of the force that acted on the body per unit area.

Unit

As we have discussed that stress is the ratio of force and area. Thus, its SI unit is N/m2 or Pascal (Pa).

The dimensional formula for stress is ML-1T-2

## How is thermal stress produced?

The thermal stress produced within an object depends on the fact that when it is subjected to rapid heating or cooling, then it is not possible for the overall surface of the object to have the same temperature level all at once. This is so because there exists a difference in the level of the temperature at the initial stage when external heating or cooling is provided.

Basically, under this process, actually what happens is – due to rapid heating or cooling, the outer surface, which is in direct contact, is more likely to have thermal expansion and contraction than the other part.

• Let us understand this in a better way:

Consider that we have a metallic cylinder to which external heat is provided. So, as the heating action takes place, the temperature of the outer surface of the cylinder will start to increase while the interior middle portion does not show a significant change in temperature initially.

But after a certain point of time, when heating continues, the centre part will also have a temperature rise, and the overall surface of the cylinder will attain the same level of temperature. And in reaction to this temperature, the material expands. This poses deformation to the object in terms of expansion. Thus the production of stress takes place.

So, we can conclude that thermal stress is the result of thermal expansion or contraction. The thermal expansion coefficient is the crucial factor according to which the material expands or contracts. Thermal Stress is the rate of change of physical dimension according to the change in temperature.

You must note here that the value of this coefficient is different for different materials, where molecular interaction plays a vital role.

### Calculation of Thermal Stress

We denote thermal stress as σ and we can calculate it as:

σ = (difference in temperature * thermal expansion coefficient * Young’s modulus of material)/ Actual temperature

Here,

• ΔT is the change in temperature where Tf and Ti are the final and initial temperature, respectively,
• α denotes the thermal expansion coefficient,
• Y represents Young’s Modulus

Thus, the thermal stress will be given as: ### Applications

The various applications of thermal stress are as follows:

• Thermostats
• Thermometers
• Bimetallic strips
• Power Lines
• Railway tracks

In all the above-given examples, the temperature, in effect, plays a crucial role. Thus, we can say thermal stress is a vital factor in our day-to-day life.