Short Answer:
Thermal stresses are the stresses that develop in a material or structure when it experiences a change in temperature and is not allowed to freely expand or contract. These stresses occur because of the thermal expansion or contraction of materials under temperature variation.
In simple words, when a body is heated, it tends to expand, and when cooled, it tends to contract. If this expansion or contraction is restricted, internal stresses are generated inside the material, called thermal stresses. They are very important in engineering design because temperature changes can cause failure, distortion, or cracking in components such as boilers, engines, and bridges.
Detailed Explanation:
Thermal Stresses
Thermal stresses are the internal stresses that develop within a body due to changes in temperature. All materials expand when heated and contract when cooled. This change in dimension due to temperature is known as thermal expansion. However, if a body is constrained and cannot freely expand or contract, internal resistance develops, which produces stress inside the material. These stresses are called thermal stresses.
Thermal stresses play a vital role in mechanical and structural engineering because components often operate under fluctuating temperatures. For example, steam pipes, pressure vessels, engine parts, turbine blades, and bridges are frequently exposed to temperature variations, leading to thermal stresses that can cause deformation or even failure if not properly accounted for.
Cause of Thermal Stresses
Thermal stresses are caused by non-uniform temperature distribution or restraint against thermal deformation.
- Non-uniform Temperature Distribution:
When different parts of a body are subjected to different temperatures, they expand or contract differently. This uneven expansion creates internal stresses within the material. - Restriction of Expansion or Contraction:
If a material is rigidly fixed at both ends and its temperature changes, it cannot expand or contract freely. The restriction develops internal compressive or tensile stresses depending on whether the temperature increases or decreases.
Derivation of Thermal Stress Formula
Let a uniform bar of length and cross-sectional area be rigidly fixed at both ends and subjected to a temperature change .
If the bar were free to expand, the increase in length due to thermal expansion would be:
Where,
= Coefficient of linear expansion (per °C)
= Temperature change (°C)
But since the bar is fixed, it cannot expand. Hence, compressive stress develops inside it to resist this expansion.
The stress developed, called thermal stress, is given by:
Where,
= Thermal stress (N/m²)
= Young’s modulus of the material (N/m²)
= Coefficient of linear expansion
= Change in temperature
Thermal strain (if free expansion is allowed) is:
Thus, thermal stress can also be expressed as:
This equation shows that the thermal stress increases with the material’s elasticity (E), coefficient of expansion (α), and temperature change (ΔT).
Types of Thermal Stresses
- Uniform Thermal Stress:
- Occurs when the entire body is subjected to a uniform temperature change but is completely restrained.
- The stress is same throughout the body.
- Differential Thermal Stress:
- Occurs when temperature varies from one part of the body to another (non-uniform heating or cooling).
- Different parts expand or contract differently, creating uneven internal stresses.
Effects of Thermal Stresses
Thermal stresses can cause the following effects on engineering structures and components:
- Dimensional Changes:
Expansion or contraction leads to distortion and misalignment in mechanical assemblies. - Cracks and Fracture:
Repeated heating and cooling can create fatigue cracks, especially in brittle materials. - Warping and Bending:
Non-uniform heating can cause differential expansion, leading to bending or warping of components. - Loss of Strength:
High temperatures reduce the strength and stiffness of materials, making them more prone to failure. - Thermal Fatigue:
Repeated thermal cycling can weaken materials over time, leading to eventual failure.
Examples of Thermal Stresses
- Steam Pipes and Boilers:
When a steam pipe is heated suddenly, the inner surface expands faster than the outer surface, causing stress in the material. - Bridges and Rail Tracks:
During hot weather, expansion can cause buckling, while contraction during cold weather can cause cracking if expansion joints are not provided. - Turbine Blades:
Rapid heating and cooling in turbines produce cyclic thermal stresses that can lead to material fatigue. - Concrete Structures:
When exposed to sunlight, the outer surface of concrete expands faster than the inner part, generating internal stresses that can cause cracks.
Factors Affecting Thermal Stresses
- Material Properties:
Materials with higher Young’s modulus (E) and thermal expansion coefficient (α) develop higher thermal stresses. - Temperature Difference:
The larger the temperature change (ΔT), the higher the induced thermal stress. - Constraints or Restraints:
The degree of restraint against expansion or contraction directly affects stress magnitude. - Shape and Size of the Component:
Thicker components experience greater temperature gradients, resulting in higher stresses. - Rate of Heating or Cooling:
Rapid temperature changes create more stress because different parts of the material expand or contract at different rates.
Methods to Reduce Thermal Stresses
- Use of Expansion Joints:
Expansion joints are provided in long pipelines, bridges, and railways to allow free expansion and contraction. - Controlled Heating and Cooling:
Gradual temperature changes prevent the development of sudden temperature gradients. - Selection of Suitable Materials:
Materials with low coefficients of expansion and high ductility should be used in temperature-varying environments. - Stress Relieving Heat Treatments:
Processes like annealing and tempering are used to minimize residual thermal stresses. - Proper Design:
Components should be designed with clearances, flexibility, and suitable supports to accommodate thermal movement.
Conclusion
Thermal stresses are internal forces developed in materials when their expansion or contraction due to temperature changes is restricted. They depend on the material properties, temperature change, and boundary conditions. Uncontrolled thermal stresses can lead to bending, cracking, and even failure of structures. By providing expansion joints, using proper materials, and ensuring controlled heating and cooling, engineers can minimize thermal stresses. Therefore, understanding thermal stress is essential for designing safe and efficient components that operate under varying temperature conditions.